Wavelength halving in a transition between standing waves and traveling waves

conditions for Turing and wave instabilities in reaction-diffusion systems

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to [Formula: see text], gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br₂. The present studies suggest that the distribution of the inhibitor, Br^-, which is produced from Br₂, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Unraveling the physiochemical nature of colloidal motion waves among silver colloids

Traveling waves are common in biological and synthetic systems, including the recent discovery that silver (Ag) colloids form traveling motion waves in H₂O₂ and under light. Here, we show that this colloidal motion wave is a heterogeneous excitable system. The Ag colloids generate traveling chemical waves via reaction-diffusion, and either self-propel through self-diffusiophoresis ("ballistic waves") or are advected by diffusio-osmotic flows from gradients of neutral molecules ("swarming waves"). Key results include the experimental observation of traveling waves of OH^- with pH-sensitive fluorescent dyes and a Rogers-McCulloch model that qualitatively and quantitatively reproduces the key features of colloidal waves. These results are a step forward in elucidating the Ag-H₂O₂-light oscillatory system at individual and collective levels. In addition, they pave the way for using colloidal waves either as a platform for studying nonlinear phenomena, or as a tool for colloidal transport and for information transmission in microrobot ensembles.

Microfluidic compartmentalization of diffusively coupled oscillators in multisomes induces a novel synchronization scenario

Multisome compartments encapsulating the Belousov–Zhabotinsky reaction produced by microfluidics arranged in 1D arrays showed a novel type of global synchronization.

Back and forth invasion in the interaction of Turing and Hopf domains in a reactive microemulsion system

Pattern formation is studied numerically for a reactive microemulsion when two parts of the system with different droplet fractions are initially put into contact.

Cross-diffusion in the two-variable Oregonator model

We explore the effect of cross-diffusion on pattern formation in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction. For high negative cross-diffusion of the activator (the activator being attracted towards regions of increased inhibitor concentration) we find, depending on the values of the parameters, Turing patterns, standing waves, oscillatory Turing patterns, and quasi-standing waves. For the inhibitor, we find that positive cross-diffusion (the inhibitor being repelled by increasing concentrations of the activator) can induce Turing patterns, jumping waves and spatially modulated bulk oscillations. We qualitatively explain the formation of these patterns. With one model we can explain Turing patterns, standing waves and jumping waves, which previously was done with three different models.

Design and control of patterns in reaction-diffusion systems

We discuss the design of reaction-diffusion systems that display a variety of spatiotemporal patterns. We also consider how these patterns may be controlled by external perturbation, typically using photochemistry or temperature. Systems treated include the Belousov-Zhabotinsky (BZ) reaction, the chlorite-iodide-malonic acid and chlorine dioxide-malonic acid-iodine reactions, and the BZ-AOT system, i.e., the BZ reaction in a water-in-oil reverse microemulsion stabilized by the surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT).

Geometry-induced pulse instability in microdesigned catalysts: the effect of boundary curvature

We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and we trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.

Complex patterns in reactive microemulsions: self-organized nanostructures?

In a reverse microemulsion consisting of water, oil (octane), an anionic surfactant [aerosol OT (AOT)], and the reactants of the oscillating Belousov-Zhabotinsky (BZ) reaction, a variety of complex spatiotemporal patterns appear. These include traveling and standing waves, spirals that move either toward or away from their centers, spatiotemporal chaos, Turing patterns, segmented waves, and localized structures, both stationary and oscillatory. The system consists of nanometer-sized droplets of water containing the BZ reactants surrounded by a monolayer of AOT, swimming in a sea of oil, through which nonpolar BZ intermediates can diffuse rapidly. We present experimental and computational results on this fascinating system and comment on possible future directions for research.